Regularized Inverse Near-Field Synthesis of Antenna Currents Using RWG Basis Functions

Inverse electromagnetic source problems are inherently ill-posed, as small perturbations in the measured or prescribed fields can lead to large variations in the reconstructed current distributions, necessitating appropriate regularization to suppress non-physical and superdirective solutions. In this work, an inverse Method of Moments (MoM) formulation [1] based on Rao–Wilton–Glisson (RWG) basis functions [2] are developed for near-field antenna pattern synthesis. The forward operator is constructed by mapping RWG surface current coefficients to the near electric field through a dipole-based radiation approximation, yielding a linear but severely ill-conditioned inverse problem.
The resulting inverse formulation is solved using Tikhonov regularization [3], which stabilizes the solution by balancing field fidelity against current smoothness. The regularization parameter is selected using the classical L-curve criterion [4], which is shown to provide a stable and physically meaningful trade-off between the residual norm and the solution norm for the proposed inverse MoM framework. Numerical results demonstrate accurate synthesis of a near-field sector beam spanning approximately ±60° in angle, with the synthesized IE_yI distribution closely matching the prescribed field profile. The reconstructed RWG surface currents remain spatially smooth and bounded in magnitude, indicating effective suppression of non-physical and superdirective solutions.
The proposed approach offers a robust and computationally efficient framework for inverse near-field antenna synthesis using surface integral formulations, and provides a validated foundation for future extensions to electrically large structures, inverse antenna–metamaterial design, and more complex inverse radiation control problems.

 

Fig.1: L curve for obtaining an appropriate 𝜆

 

Fig.2: Synthesized surface current for sector pattern for 𝜃=60° at 𝜌=0.01𝜆

Fig.3: Comparison plot of desired and synthesized sector pattern for 𝜃=60° at 𝜌=0.01𝜆

 

References
[1] S. H. Raad, J. S. Meiguni, and R. Mittra, “Inverse MoM Approach to Near-Field Prediction and RFI Estimation in Electronic Devices With Multiple Radiating Elements,” IEEE Access, vol. 11, pp. 21313–21325, 2023.
[2] S. Rao, D. Wilton, and A. Glisson, “Electromagnetic Scattering by Surfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409–418, 1982.
[3] D.-H. Han, X.-C. Wei, D. Wang, W.-T. Liang, T.-H. Song, and R. X. K. Gao, “A Phase less Source Reconstruction Method Based on Hybrid Dynamic Differential Evolution With Least Square and Regularization,” IEEE Transactions on Electromagnetic Compatibility, vol. 66, no. 2, pp. 566–573, 2024.
[4] P. C. Hansen, “The L-curve and its use in the numerical treatment of inverse problems,” SIAM Review, vol. 34, no. 4, pp. 561–580, 1992.